Recent content by Hohen

I think I get it. The speed of ##P_{bottom}## relative to the ground is 0. The speed of ##P_{center}## relative to the ##P_{bottom}## is ##R⋅\omega## ##P_{top}##'s speed relative to the ##P_{center}## is ##R⋅\omega## So ##P_{center}##'s speed relative to the ground is ##2⋅R⋅\omega## Another...

I'm stuck with this. The only relation I found between ##x_2## and ##\theta_2## is ##x_2 = \theta_2 ⋅ R## So with derivation ##\frac{d(x_2)}{dt} = \dot \theta_2 ⋅ R## About ##x_1## and ##x_2## all I can think of that ##x_2## travels half a distance as ##x_1##.

That means my calculation with the Lagrangain is correct, I just used wrong generalized coordinates?

One last question: I digged into Lagrangian mechs. a little bit. The second task at this problem to write the Lagrangian equation of the system. Here is how I calculated: $$ 0 = \frac {d} {dt} (\frac {∂L}{∂\dot x}) - \frac {∂L}{∂x} $$ ##L = KE-PE##, where ##PE = -m1⋅g## $$KE =...

Like this? ##I_2⋅\omega_2^2=(m_2⋅R^2)⋅(\frac{v}{2R})^2=p_2⋅\dot \theta_2^2=(m_2⋅x _2^2)⋅(\frac{\dot x_2}{2x_2})^2## The velocities are devided with ##2## because ##v## is the velocity of the plank (so it equals vrot of the cylinders)

yes Okay, but why the amplitude isn’t in the equation? It doesn't matter for the frequency/time period how long the initial distance was when the system started moving? The second object in this problem was to write the Lagrangian equation of the system. That’s why I calculated out.

It was too hard (and I have no time) to calculate the period with Newton's laws. Instead I tried Lagrangian mechanics. Can you help me with this? Here is how I calculated: $$ 0 = \frac {d} {dt} (\frac {∂L}{∂ Ẋ}) - \frac {∂L}{∂x} $$ $$ L = KE-PE$$ $$PE = \frac{1}{2} ⋅ k ⋅ x^2$$ $$KE =...

Thank you! Wild guess: "cylinders roll past the equilibrium point" They leave equilibrium when they start rolling? So due action-reaction the kinetic energy is in balance between the plank and cylinders. My guess is based on the observation that the string accelerates and decelerates the plank...

Here is the picture on the system. I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position. In the thread...

Thank you very much for your help!

uh I need time to process this but… I calculated the acceleration. The result I got is $$a =g⋅ \frac {8(m1)} {8m1+8(m2)+3(m3)+3(m4)}$$ Am I correct? I attached 2 pictures about how I got this result on paper.

Then half of a but I still don't understand complitly. I drew another picture: ß is the angular acceleration. So the equation a = R⋅ß gives me the acceleration in a point with R distance from point 0 (a = 0)? Is this equation only true on the yellow line? Is this somehow related to the x and...

It's always 0.

Oh sh.. I made a typo indeed, sry :D So otherwise is it correct? If it is I know parametrically the acceleration of the plank. The rotational acceleration of the outer edge of the cylinder is the same as the plank's acceleration, right? I analyzed a similar problem found on the internet. It said...

I meant to write this.